A041547 Denominators of continued fraction convergents to sqrt(291).

1, 17, 579, 9860, 335819, 5718783, 194774441, 3316884280, 112968839961, 1923787163617, 65521732402939, 1115793238013580, 38002491824864659, 647158154260712783, 22041379736689099281, 375350613677975400560, 12783962244787852718321

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,580,0,-1).

Formula

G.f.: -(x^2-17*x-1) / (x^4-580*x^2+1). - Colin Barker, Nov 18 2013

a(n) = 580*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[291], 40]] (* Harvey P. Dale, Apr 20 2012 *)
CoefficientList[Series[(1 + 17 x - x^2)/(x^4 - 580 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 20 2013 *)

Prog

(Magma) I:=[1, 17, 579, 9860]; [n le 4 select I[n] else 580*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A041546, A040273.

Sequence in context: A191865 A249862 A056771 * A041544 A202407 A009709

Adjacent sequences: A041544 A041545 A041546 * A041548 A041549 A041550

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved